This report is an example of the report your team is supposed to produce
A few years back, Idaho joined states that require students take a college entrance exam for graduation. Furthermore, the state of Idaho sets aside a day each year for juniors to take the exam paid for by the state. While students could take the ACT instead of the SAT, the SAT has become the exam taken by almost all juniors in the state (93% in 2017). Since Idaho adopted this requirement, the state's average score has decreased significantly. Because of this, I wanted to explor the association with average score and percent taking the test.
Linear Model:
This scatterplot shows a strong, negative association, but it does look to have a curve to it.
The correlation, R = 0.8675, confirms a strong linear assoiation. Whith R^{2 }= 75.3% we can say that 75.3% of the variation in state SAT scores can be explained by percent taking the test. The slope shows us that, on average, a states score drops 2.27 points for each percent increase in those taking the tesc.
Simple linear regression results:
Dependent Variable: Total Independent Variable: Participation Total = 1216.6391  2.2746766 Participation Sample size: 51 R (correlation coefficient) = 0.86753981 Rsq = 0.75262533 Estimate of error standard deviation: 46.470993 Parameter estimates:
Analysis of variance table for regression model:

The residual plot has a definate curved pattern to it. This sugests we might be able to find a better model.
Power Model:
By reexpressing both x and y using the natural logarithm, the scatterplot shows a stronger linear model than before.
The correlation, R = 0.9141, has also improved significantly. As has R^{2 }= 83.6%.
Simple linear regression results (w/ transformation):
Dependent Variable: ln(Total) Independent Variable: ln(Participation) ln(Total) = 7.1785279  0.052376794 ln(Participation) Sample size: 51 R (correlation coefficient) = 0.91407 Rsq = 0.83552397 Estimate of error standard deviation: 0.033396834 Parameter estimates:
Analysis of variance table for regression model:

The residual plot shows no pattern but there might be one outlier. Because this possible outlier is near the center of the data, it only has a little leverage. Therefore it might make the correlation look weaker than it is, but it will have little affect on the slope.
Already a member? Sign in.